(\partial)/(\partial p)(arctan(pqr))

解答

\frac{\partial}{\partial p} (arctan (pq r))

\frac{q r}{p ^{2} q ^{2} r ^{2} + 1}

求解步骤

\frac{\partial}{\partial p} (arctan (pq r))

将

q, r

视为常数

使用连锁律:

\frac{1}{( pq r ) ^{2} + 1} \frac{\partial}{\partial p} (pq r)

= \frac{1}{( pq r ) ^{2} + 1} \frac{\partial}{\partial p} (pq r)

\frac{\partial}{\partial p} (pq r) = q r

= \frac{1}{( pq r ) ^{2} + 1} q r

化简

\frac{1}{( pq r ) ^{2} + 1} q r : \frac{q r}{p ^{2} q ^{2} r ^{2} + 1}

= \frac{q r}{p ^{2} q ^{2} r ^{2} + 1}

- cot (x) = \frac{v ^{'}}{v ^{2}}

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